Title: Unfolding Orthogonal Polyhedra Speaker: Robin Flatland Abstract: An unfolding of a polyhedron is a set of cuts that can be applied to its surface so that it can be unfolded flat as a single piece without overlap. Applications of polyhedra unfolding arise in manufacturing processes that construct three-dimensional objects by bending sheet metal. It is a long unsolved problem to determine whether every polyhedron may be unfolded. In this talk, the focus is on recent progress in unfolding orthogonal polyhedra, a class of polyhedra whose faces all meet at right angles. An algorithm will be presented that proves every orthogonal polyhedron of genus zero may be unfolded. For a polyhedron of $n$ vertices, portions of the unfolding are rectangular strips which, in the worst case, may need to be as thin as \epsilon = 1 / 2^{\Omega(n)}.